Complex numbers Questions and Answers

Use the graph below to determine the equation of the circle in a center radius form and b general form 10 40 0 2 46 4 2 a Type the equation in center radius form Simplify your answer

Use the graph below to determine the equation of the circle in a center radius form and b general form 10 16 3 6 32 5 a Type the equation in center radius form Simplify your answer

Find the center radius form of the equation of the circle described and graph it center 0 2 radius 2 Type the center radius form of the equation of the circle Type an equation Simplify your answer 10

1 Determine the amplitude period phase shift and midline of the given function Clearly label your answers 1 y cos 3x 6

Solve the equation 813x 3 729x 2

Use the definition of inverses to determine whether f and g are inverses 1 f x 3x 11 g x 3X 11 Are the given functions inverses O Yes No

Rewrite the expression In 39 In 6 so that it includes the expressions In 3 and 39 and 6 do not appear inside a natural logarithm Expression

Use the properties of logarithms to rewrite the expression Simplify the result as much as possible Assume all variables represent positive real numbers 5r7 25 log2 Select the correct choice below and if necessary fill in the answer box to complete your choice log2 5r cannot be simplified

If 12 g of a radioactive substance are present initially and 8 yr later only 6 0 g remain how much of the substance to the nearest tenth of a gram will be present after 15 yr After 15 yr there will beg of the radioactive substance Do not round until the final answer Then round to the nearest tenth as needed HID

Write in logarithmic form 35 243 What is the equivalent logarithmic form log 3 Simplify your answers Type integers or fractions

Find the half life of a radioactive element which decays according to the function 0 0304t A t Ape where t is the time in years 2 The half life of the element is years Round to the nearest tenth

Let f x 7x 18 and let g x 13x 1 Find f g 7

Given f x Inx evaluate a f e4 b f eln 5 c f e6 In 5 a f e4 4 Type an exact ans b f eln 5 Type an exact ans

Find the area of the triangle below Area 30 1 a 6 2 b 8 ab sin 30

Graph the function and determine whether the function is one to one using the horizontal line test f x 9 x Graph the function f x 9 x Use the graphing tool to graph the function Click to enlarge graph 10

Use the graph to identify zeros and multiplicity Order your zeros from least to greatest 6 5 4 3 Zero at Zero at Zero at Zero at 6 5 4 3 2 1 H 3 4 5 6 2 3 4 5 6 with multiplicity with multiplicity with multiplicity with multiplicity

What are the steps for solving the equation log 4x 2 2 An exponential equation equivalent to log 4x 2 2 is Select Simplifying the side with the exponent gives Select The solution is x Select

a Find the decibel rating of a sound d 10 log having intensity 1 000 000l where lo is the initial intensi lo b If the intensity of a sound is tripled by how much is the decibel rating increased a Find the decibel rating of a sound having intensity 1 000 000 where lo is the initial intensity The decibel rating of this sound is

Use the change of base theorem to find the logarithm log 83 Use the change of base theorem to rewrite the given expression in terms of n log 83 Do not evaluate Do not simplify

1 The magnitude of an earthquake measured on the Richter scale is log 107 where is the amplitude registered on a seismograph 100 km from the epicenter of the earthquake and lo is 10 10 the amplitude of a certain small size Find the Richter scale rating for an amplitude of 100 000 000 The magnitude R measured on the Richter scale is

Given f x In x evaluate a f e4 b f eln 5 c f e6 In 5 a 1 4 Type an

Find the value In 88 In 25 In 88 In 25

Find the value 16 In ve 16 e 0 In Ve Simplify your answer Type an integer or a fra

Find the value 1 In 2 In 2 e

Use a calculator to find approximations a log 347 3 b log 34 73 of the common logarithms c log 3 473 a log 347 3 Simplify your answer Round to four decimal places as needed

Find the exact value log 0 0001 log 0 0001

Find the exact value log 10 5 10 5 I 10

3 A stereo system loses its value each month after it is purchased Its value as a function of time in months is modelled by V 1 1500 0 90 a Sketch the graph of the function b Determine the i Domain ii Range c What is the value of the stereo system after 3 months

Rationalize the denominator 7 7 7 7 7 7 7 7 Simplify your answer Use integers or fractions for any numbers in th

To rationalize the denominator of 1 2 6 8 by what number should the numerator and denominator be multiplied The numerator and denominator should be multiplied by

Rationalize the denominator 6 8 6 6 8 6 Simplify your answer Type an exact answer using radicals as needed Use integers or fractions for

Rationalize the denominator 3 3 7 45 45 Simplif you juor Tuno on avant apowIGE a radioola

Rationalize the denominator Assume all variables are positive 5 3 2

Click here to watch the video Rationalize the denominator If possible simplify the rationalized expression by dividing the numerator and denominator by th greatest common factor 1 11

Multiply and simplify 2 2 7 7 2 5 7 2 2 7 7 2 5 7

Add Assume all variables are greater than or equal to zero 9 3 64x 7 x

Write th h 2 A

K a Find the inverse of the function below on the given interval and write it in the form y f x b Verify the relationships f x x and f x x f x x 36 for x50 a f x x 36 b Verify the relationship f x x Select the correct choice below and fill in the answer box es to complete your choice OA B x 36 Type integers or simplified fractions A X F x x 36 36 x Verify the relationship f f x x Select the correct choice below and fill in the answer box es to complete your choice B f x 36 36 Type integers or simplified fractions Points 0 4 of 1 X 19 33 of 24 pois

x 6x 16

x 5x 4 0

x 11x 30 0

Classify the polynomial by its degree and number of terms

k 3k 1 k 8

ssify the polynomial by its degree and number of terms

Classify the polynomial by its degree and number of terms

4 Given y 3x 24x 36 a 5 points Find the x and y intercepts Do not round b 4 points Find the vertex Do not round c 5 points Use the information from part a and b to graph the quadratic equation Plea label your points

10 points Solve the following system of equations 2y 6x 20 x 4y 40 0

Combine all 10 equations into one piecewise function Include correct domains for each part of the piecewise function y 2 x 1 5 x 3 y x 5 8 3 x 7

Use the properties of logarithms to condense the following logarithmic expression The solution should be a single logarithm with a coefficient of 1 Where possible evaluate logarithmic expressions 2 log 4 log b log 5 2 log 4 log b log 5

12 The coordinates of point A are 1 5 If the slope of the line is name the coordinates of another point on the line